The present invention relates to a new and distinct cultivar of chrysanthemum plant, botanically known as Chrysanthemum×morifolium Ramat., commercially known as a garden mum, and hereinafter referred to by the cultivar denomination ‘Zanmugrape’. ‘Zanmugrape’ is a product of a breeding and selection program for outdoor pot mums (garden mums) which had the objective of creating new cultivars with a double type inflorescence, a natural season flowering date around October 1, blooming for a period of 5 weeks. ‘Zanmugrape’ is a seedling resulting from a cross of the female parent 22173 with the male parent 17006. Plants of the new cultivar ‘Zanmugrape’ differ from plants of the parents in the following characteristics. (1) Ray-floret color. And (2) Natural season flowering date. (1) Plants of the seedling have purple colored ray-florets, while plants of the female parent have pink colored ray-florets, and plants of the male parent have salmon colored ray-florets. (2) Plants of the seedling flower two weeks earlier in the season than those of the female parent, and one week earlier than those of the male parent. The new and distinct cultivar was discovered and selected as a flowering plant by Henricus Cornelius Maria Jacobs on a cultivated field in Rijsenhout, The Netherlands in 2010. The first act of asexual production of ‘Zanmugrape’ was accomplished when vegetative cuttings from the initial selection in 2010 were propagated further in a controlled environment in Rijsenhout, The Netherlands. The new cultivar has been found to retain its distinctive characteristics through successive propagations.